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課程名稱 (中文) 隨機過程
(英文) Random Variable & Stochastic Process
開課單位 電機工程學系
課程代碼 E4070
授課教師 龔宗鈞
學分數 3.0 必/選修 選修 開課年級 大四
先修科目或先備能力:工程數學(微積分、矩陣、富氏分析)
課程概述與目標:使學生了解隨機變數與隨機過程之數學理論與物理觀念,並能夠應用於系統上之分析與設計。
教科書 作者 : Peyton Z. Peebles, Jr.
書名 : Probability, Random Variables and Random Signal Principles
出版社 : McGraw Hill(ISBN 0-07-118181-4)
參考教材
課程大綱 學生學習目標 單元學習活動 學習成效評量 備註
單元主題 內容綱要
1 Probability 1. Probability Introduced Through Sets and Relative Frequency
2. Joint and Conditional Probability
To understand: experiments and sample spaces, discrete and continuous sample spaces, events, probability definition and axioms, joint and conditional probability, Bayes' theorem.
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    2 Probability 1. Independent Events
    2. Combined Experiments
    3. Bernoulli Trials
    To understand: two events, multiple events, properties of independent events, combined sample space, events on the combined sample space, Bernoulli trials.
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    3 The Random Variable 1. The Random Variable Concept
    2. Distribution Function
    3. Density Function
    To understand: definition of random variable, conditions for a function to be a random variable, discrete and continuous random variable, mixed random variable, distribution function, density function.
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    4 The Random Variable 1. The Gaussian Random Variable
    2. Other Distribution and Density Examples
    3. Conditional Distribution and Density Function
    To understand: the Gaussian random variable, binomial distribution, Possion distribution, uniform distribution, conditional distribution, conditional density function.
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    5 Operations on One Random Variable (RV) 1. Expection
    2. Moments
    To understand: expected value of a RV, expected value of a function of a RV, moments about the origin, central moments, variance and skew, Chebychev's inequality.
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    6 Operations on One Random Variable (RV) 1. Transformations of a Random Variable To understand: monotonic transformations of a continuous RV, nonmonotonic transformations of a continuous RV, transformation of a discrete RV.
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    7 Multiple Random Variables 1. Vector Random Variables
    2. Joint Distribution and Its Properties
    To understand: joint distribution function and its properties, marginal distribution functions.
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    8 Multiple Random Variables 1. Joint Density and Its Properties
    2. Conditional Distribution and Density
    To understand: joint density function and its properties, marginal density functions, conditional distribution and density.
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    9 Random Variables 1. Probability
    2. Random Variables
    3. Operations on One Random Variable
    4. Multiple Random Variables
    To understand:
    1. Probability
    2. Random Variables
    3. Operations on One Random Variable
    4. Multiple Random Variables
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    10 Multiple Random Variables 1. Statistical Independence
    2. Distribution and Density of a Sum of RVs
    3. Central Limit Theorem
    To understand: statistical independence of RVs, distribution and density of a sum sum of two RVs, central limit theorem.
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    11 Operations on Multiple Random Variables 1. Expected Value of a Function of Random Variables
    2. Joint Characteristic Functions
    3. Joint Gaussian Random Variables
    To understand: joint moments about the origin, joint characteristic functions, joint Gaussian RVs.
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    12 Operations on Multiple Random Variables 1. Transformations of Multiple Random Variables
    2. Sampling and Some Limit Theorems
    To understand: transformations of multiple RVs, sampling and some limit theorems.
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    13 Random Processes-Temporal Characteristics 1. The Random Process Concept
    2. Stationarity and Independence
    To understand: classification of processes, statistical independence, first-order stationary process, second-order and wide-sense stationarity, N-order and strict-sense stationarity, time average and ergodicity.
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    14 Random Processes-Temporal Characteristics 1. Correlation Functions
    2. Gaussian Random Processes
    To understand: autocorrelation function and its properties, cross-correlation function and its properties, covariance functions.
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    15 Random Processes-Spectral Characteristics 1. Power Density Spectrum and Its Properties
    2. Relationship between Power Spectrum and Autocorrelation Function
    3. Cross-Power Density Spectrum and Its Properties
    To understand: the power density spectrum and its properties, bandwidth of the power density spectrum, relationship between power spectrum and autocorrelation function, the cross-power density spectrum and its properties.
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    16 Random Processes-Spectral Characteristics 1. Power Spectrum for Discrete-Time Processes and Sequences
    2. Some Noise Definitions
    To understand: discrete-time processes, discrete-time sequences, white noise and colored noise.
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    17 Linear Systems with Random Inputs 1. Linear System Fundamentals
    2. Random Signal Response of Linear System
    3. Spectral Characteristics of System Response
    To understand: mean and mean-squared value of system response, autocorrelation function of response, cross-correlation functions of input and output, power density spectrums of response, cross-power density spectrums of input and output.
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    18 Random Processes-Spectral Characteristics 1. Random Processes-Temporal Characteristics
    2. Random Processes-Spectral Characteristics
    3. Linear Systems with Random Inputs
    To undserstand: random processes-temporal characteristics, random processes-spectral characteristics, linear systems with random inputs.
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